\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t} \]

↓

\[x + \frac{-2}{\frac{\frac{z}{y}}{0.5} - \frac{t}{z}} \]

(FPCore (x y z t)
 :precision binary64
 (- x (/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))))

↓

(FPCore (x y z t)
 :precision binary64
 (+ x (/ -2.0 (- (/ (/ z y) 0.5) (/ t z)))))

double code(double x, double y, double z, double t) {
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
}

↓

double code(double x, double y, double z, double t) {
	return x + (-2.0 / (((z / y) / 0.5) - (t / z)));
}

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x - (((y * 2.0d0) * z) / (((z * 2.0d0) * z) - (y * t)))
end function

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((-2.0d0) / (((z / y) / 0.5d0) - (t / z)))
end function

public static double code(double x, double y, double z, double t) {
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
}

↓

public static double code(double x, double y, double z, double t) {
	return x + (-2.0 / (((z / y) / 0.5) - (t / z)));
}

def code(x, y, z, t):
	return x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)))

↓

def code(x, y, z, t):
	return x + (-2.0 / (((z / y) / 0.5) - (t / z)))

function code(x, y, z, t)
	return Float64(x - Float64(Float64(Float64(y * 2.0) * z) / Float64(Float64(Float64(z * 2.0) * z) - Float64(y * t))))
end

↓

function code(x, y, z, t)
	return Float64(x + Float64(-2.0 / Float64(Float64(Float64(z / y) / 0.5) - Float64(t / z))))
end

function tmp = code(x, y, z, t)
	tmp = x - (((y * 2.0) * z) / (((z * 2.0) * z) - (y * t)));
end

↓

function tmp = code(x, y, z, t)
	tmp = x + (-2.0 / (((z / y) / 0.5) - (t / z)));
end

code[x_, y_, z_, t_] := N[(x - N[(N[(N[(y * 2.0), $MachinePrecision] * z), $MachinePrecision] / N[(N[(N[(z * 2.0), $MachinePrecision] * z), $MachinePrecision] - N[(y * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_] := N[(x + N[(-2.0 / N[(N[(N[(z / y), $MachinePrecision] / 0.5), $MachinePrecision] - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}

↓

x + \frac{-2}{\frac{\frac{z}{y}}{0.5} - \frac{t}{z}}

Original	11.9
Target	0.1
Herbie	0.1

Derivation

Initial program 11.9
\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t} \]
Simplified0.1
\[\leadsto \color{blue}{x + \frac{-2}{\frac{\frac{z}{y}}{0.5} - \frac{t}{z}}} \]
Proof
(+.f64 x (/.f64 -2 (-.f64 (/.f64 (/.f64 z y) 1/2) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (Rewrite<= metadata-eval (neg.f64 2)) (-.f64 (/.f64 (/.f64 z y) 1/2) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (/.f64 z y) (Rewrite<= metadata-eval (/.f64 1 2))) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (/.f64 z y) (/.f64 (Rewrite<= *-inverses_binary64 (/.f64 z z)) 2)) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (/.f64 z y) (Rewrite<= associate-/r*_binary64 (/.f64 z (*.f64 z 2)))) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (Rewrite<= associate-/r*_binary64 (/.f64 z (*.f64 y (/.f64 z (*.f64 z 2))))) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 z (/.f64 z (*.f64 z 2))) y)) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 z (*.f64 z 2)) z)) y) (/.f64 t z)))): 20 points increase in error, 1 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 z 2) z)) z) y) (/.f64 t z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (/.f64 (*.f64 (*.f64 z 2) z) z) y) (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 t z)))))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (/.f64 (*.f64 (*.f64 z 2) z) z) y) (*.f64 (Rewrite<= *-inverses_binary64 (/.f64 y y)) (/.f64 t z))))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (/.f64 (*.f64 (*.f64 z 2) z) z) y) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y t) (*.f64 y z)))))): 34 points increase in error, 3 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (-.f64 (/.f64 (/.f64 (*.f64 (*.f64 z 2) z) z) y) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 (*.f64 y t) z) y))))): 7 points increase in error, 22 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (/.f64 (*.f64 (*.f64 z 2) z) z) (/.f64 (*.f64 y t) z)) y)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (/.f64 (neg.f64 2) (/.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)) z)) y))): 0 points increase in error, 0 points decrease in error
(+.f64 x (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 2 (/.f64 (/.f64 (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)) z) y))))): 0 points increase in error, 0 points decrease in error
(+.f64 x (neg.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 2 y) (/.f64 (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)) z))))): 4 points increase in error, 5 points decrease in error
(+.f64 x (neg.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 y 2)) (/.f64 (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)) z)))): 0 points increase in error, 0 points decrease in error
(+.f64 x (neg.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 y 2) z) (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t)))))): 42 points increase in error, 9 points decrease in error
(Rewrite<= sub-neg_binary64 (-.f64 x (/.f64 (*.f64 (*.f64 y 2) z) (-.f64 (*.f64 (*.f64 z 2) z) (*.f64 y t))))): 0 points increase in error, 0 points decrease in error
Final simplification0.1
\[\leadsto x + \frac{-2}{\frac{\frac{z}{y}}{0.5} - \frac{t}{z}} \]

Alternatives

Alternative 1
Error	14.3
Cost	848

\[\begin{array}{l} t_1 := x - \frac{y}{z}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-123}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	7.0
Cost	712

\[\begin{array}{l} t_1 := x - \frac{y}{z}\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{z}{t} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	16.8
Cost	520

\[\begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-302}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	15.9
Cost	64

\[x \]

Error

Try it out

Target

Derivation

Alternatives

Error

Reproduce

In
Out